A box contains 15 tickets numbered 1, 2, ....... 15 . Seven tickets are drawn at random one after ot

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14.Probability

medium

A box contains $15$ tickets numbered $1, 2, ....... 15$. Seven tickets are drawn at random one after the other with replacement. The probability that the greatest number on a drawn ticket is $9$, is

${\left( {\frac{9}{{10}}} \right)^6}$

${\left( {\frac{8}{{15}}} \right)^7}$

${\left( {\frac{3}{5}} \right)^7}$

None of these

(IIT-1983)

Solution

(c) On trial, $n = 15$ since any of the $15$ numbers can be on the selected coin and $m = 9$ since the largest number is $9$ and so it can be $1$ or $2$ or $3………$ or $9$.
We have required probability $ = {\left( {\frac{9}{{15}}} \right)^7} = {\left( {\frac{3}{5}} \right)^7}.$

Standard 11

Mathematics

A box contains $25$ tickets numbered $1, 2, ……. 25$. If two tickets are drawn at random then the probability that the product of their numbers is even, is

medium

The letter of the word `$ASSASSIN$' are written down at random in a row. The probability that no two $S$ occur together is

hard

(IIT-1983)

A box contains $10$ red marbles, $20$ blue marbles and $30$ green marbles. $5$ marbles are drawn from the box, what is the probability that all will be blue?

easy

A lot consists of $12$ good pencils, $6$ with minor defects and $2$ with major defects. A pencil is choosen at random. The probability that this pencil is not defective is